The secret to picking up the best digital cameras is captured by the following equation: Best Image Quality = Megapixels X Sensor Size

Put in other words, the key thing to note about mega-pixels is that they only help in a better image quality camera if they are accompanied with big enough sensors.As far as megapixels is concerned figure out the prints that you are looking for and then consult the table below:
5 megapixels: sharp 8-by-10 inch
7 megapixels: sharp 11-by-14 inch
10 megapixels: acceptable 13-by-19 inch
14 megapixels: sharp 13-by-19 inch, acceptable 16-by-24 inch

The simple reason why DSLR's take stunning photos is because they have bigger sensors (and also because they have bigger lenses).

However for choosing the overall best camera just looking at the theoretical image quality is not good enough - what you get in practice will depend on three other factors which are
1. Response Times
2. Zoom Lens
3. Image Stabilization

Response TimesThis is typically found in the specs under the 'burst mode' or the 'continuous shooting' count in shots per second. For heavy duty action or sports photography something like 3 shots per second should be good enough - though for casual everyday use slightly lesser should also suffice.

Zoom LensThe best cameras for 2013 do not skimp on the optical zoom lens anymore. Higher optical zooms let you magnify the subjects without loosing the quality - this is different from digital zooms which degrade quality on magnification. The best sub- $200 cameras now boast of optical lenses as high as 10x or even more.

Image StabilizationHigh powered optical zoom though requires better image stabilization. The reason being that as you increase optical zoom, the slightest shakes in the camera body can result in blurry images. The best stabilization is the in-body one - though this is limited to mostly DSLR's and interchangeable lens cameras. In-body stabilization basically means that the camera is engineered to mechanically stabilize your images regardless of the lens which is attached.

The list below is a bunch of the best digital cameras of 2013, ranked by the ReviewGist Score which is based on top experts ratings from around the internet.

DSLR'sThe best DSLR's are the cameras to buy for pro-shooters. They are also the most expensive and have a huge learning curve. Consequently the DSLR'salso offer the best in class picture quality, great response times and full manual controls regarding exposure and focus. The downsides are they are typically very heavy to lug around so cannot be used for everyday shooting.

Compact System/Compact Interchangeable-Lens CamerasThe best compact system cameras also offer serious shooting without the bulk of the DSLR's. The picture quality is excellent and they are a lot cheaper than the DSLRs. However, interchangeable lens cameras lack the lens options available to DSLRs and also missing is the through-the-lens optical viewfinders.

Bridge camerasThe Bridge cameras combine the functionalities of the professional DSLRs and the consumer point and shoot cameras - and hence they are also called Prosumer cameras. Some of the less bulkier Bridge cameras which support extenal flash along with other advanced features are called Hybrid cameras.

Ultra-ZoomsUltra-Zooms are the new class of compact cameras which come with very high optical zooms (>15x). The result is some serious shooting capabilities without the hassle of changing lenses. The best ultra-zooms come with some great image stabilization also, but they are more expensive than the typical point-and-shoot and often times slightly bulky also. For a more regular use consider the best compact ultra-zooms and some of the products under this type are the best travel zoom cameras of 2013.

Compact/Point and ShootsThe best compact/point and shoot cameras are great cameras for everyday use. The list of compact/point and shoot cameras also includes some of the best beginner cameras 2013. These cameras are typically inexpensive and are great cameras for everyday use or even if you are just starting out.
Most come with automatic settings , so if you don't want to get into the gory photography details and limit yourself to casual shooting - the best point and shoots is what you should be looking for. If you are using them as a stepping stone to learn more serious photography, probably look at a compact which has manual controls.